Another week had passed by as the preparation for launching their smithing enterprise, BLOODBORNE came close.
The reasoning Kahn gave Albestros when suggesting this name was that the name implied creating something precious with your hard work and sweat & blood.
It signifies Rebirth and Perseverance.
But in reality.. It was just because he loved the Bloodborne video game as he was once Dark Souls player during his gaming days of the youth.
But since he couldn't just name the shop as Dark Souls or Sekiro : Shadows Die Twice.. Which would give a grim feeling to the business itself, he had to choose Bloodborne. And once he spread fake stories about what the name signifies, people would be more curious about the shop.